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Period: 1900 BCE to 1600 BCE
The Babylonians join the fraction party too!
At some point between 1900 and 1600, the Babylonians further developed their sexagesimal, or base-sixty system so that it could handle fractions. -
1800 BCE
The Egyptians were FIRST!
About 4000 years ago, or 1800 BC, Egyptians were using fractions with a systems that was based upon part, or what we call unit fractions. These parts were combined in order to get larger quantities. They weren't however, written as we show fractions today. Instead a symbol meaning part was placed over a hieroglyphic numeral. https://nrich.maths.org/2515 -
311 BCE
Zero the Hero
Despite the Babylonians creative way of writing fractions, they developed a way to represent zero as it was often difficult to interpret the value being shown. It should be noted though that nothing is perfect, and the difficulty of being able to tell fractions from whole numbers was still a challenge! https://nrich.maths.org/2515 -
300 BCE
Euclid's Contribution
The Euclidean Algorithm is a "procedure for finding the greatest common divisor of two numbers." It uses fractions to help solve equations by dividing the larger number by the smaller until exact division is obtained.
https://www.britannica.com/topic/Euclidean-algorithm -
100 BCE
The Chinese: our kindred fraction spirit
The book, "Nine Chapters on the Mathematical Art" explores how the Chinese mathematicians thought about and worked with fractions. Their work was quite similar to our current fractional system, with the exception of not using improper fractions but rather expressing such quantities as a mixed number. -
Period: 601 to 700
Learning from the Chinese
Manuscripts from India show an approach to writing fractions that was similar to that of the Chinese. It shows two numbers, one written on top of the other. It is important to note that there is no line or mark between the two digits. This approach soon caught on as people in Europe began expressing fractions the same way. -
850
Form is quite important...
The form in which the fractions were written, affected the arithmetic that was performed, as the fraction was interpreted dependent upon this factor. "For instance, the 'invert and multiply' rule for dividing fractions was used by the Indian mathematician Mahavira..." (Berlinghoff and Gouvêa, 2015) Berlinghoff, W. P., & Gouvêa, F. Q. (2015). Math through the ages: a gentle history for teachers and others (2nd ed.). Farmington, ME: Oxton House. -
1200
Who's LINE is it anyway??!
The horizontal fraction bar, known to some as the vinculum, can be first credited to the Arabs (although they are reported to have copied the Hindu's way of writing fractions, later improving upon this notation by adding the bar that sits between the numerator and denominator). The use of this symbol however, did not catch on until a few hundred years later. -
1202
"Liber Abaci" to some... Book of Calculation to others.
"Fibonacci's 'Liber Abaci,' an influential 13th-century European mathematics text, made extensive use of unit fractions and described various ways of converting other fractions to sums of unit fractions." Berlinghoff, W. P., & Gouvêa, F. Q. (2015). Math through the ages: a gentle history for teachers and others (2nd ed.). Farmington, ME: Oxton House. -
Period: 1401 to
Per cent = for every hundred
Decimal arithmetic originated during the 15th and 16th centuries when interest rates were quoted in hundredths. The term per cent became quite common as it was given to fractions that had a denominator of 100. The idea was reinforced as our monetary system is aligned. (Berlinghoff and Gouvêa, 2015) Berlinghoff, W. P., & Gouvêa, F. Q. (2015). Math through the ages: a gentle history for teachers and others (2nd ed.). Farmington, ME: Oxton House. -
1425
% Evolution
The symbol standing for percent has gradually evolved. It started as being a handwritten abbreviation for "per 100."(Berlinghoff and Gouvêa, 2015) Berlinghoff, W. P., & Gouvêa, F. Q. (2015). Math through the ages: a gentle history for teachers and others (2nd ed.). Farmington, ME: Oxton House. -
Wait... decimals = fractions?
Despite decimal fractions being used within Chinese and Arabic mathematics for quite sometime, the idea was not widely accepted to the West. Simon Stevin explained how simple calculations can be when using decimals in place of fractions to add whole numbers. Interestingly enough, he avoided decimals that continue on infinitely. Berlinghoff, W. P., & Gouvêa, F. Q. (2015). Math through the ages: a gentle history for teachers and others (2nd ed.). Farmington, ME: Oxton House. -
Period: to
Half-half-half-half-half-third...what?
The unit fraction approach has continued as evidenced by Russian manuscripts referencing to 1/96 as half-half-half-half-half-third. The idea was for it to be interpreted as 1/3 of 1/2 of 1/2 of 1/2 of 1/2 of 1/2 = 1/96. (Berlinghoff and Gouvêa, 2015) Berlinghoff, W. P., & Gouvêa, F. Q. (2015). Math through the ages: a gentle history for teachers and others (2nd ed.). Farmington, ME: Oxton House. -
% Evolution
The percent symbol has continued to evolve, turning into "per 0/0" next, and not long after, the word per was dropped making it simply "0/0/." The final change came when the symbol became %. (Berlinghoff and Gouvêa, 2015) Berlinghoff, W. P., & Gouvêa, F. Q. (2015). Math through the ages: a gentle history for teachers and others (2nd ed.). Farmington, ME: Oxton House. -
Vinculum 2.0
Another version of the horizontal fraction bar, or vinculum, is the diagonal slash. There are many instances of this symbol being used in place of the traditional horizontal line, however the earliest comes from the Thomas Twining's Ledger, a handwritten document. In this, transactions were listed such as 1/4 pound green tea.This symbol was used as the horizontal line was typically difficult to produce in print sources. http://jeff560.tripod.com/fractions.html -
Hello calculators? Goodbye fractions?
With the mainstream introduction of calculators, the use of decimals and their place in mathematics was quite solid. This was not to say that fractions were getting the boot. Fractions have many benefits including how they can show a relationship between two values as well describe part of a whole. We can live in a world that has a welcomed use for fractions as well as their partner-in-crime, decimals. No competition here!
